One interesting problem in graph colouring is the Erdős-Faber-Lovász conjecture, first formulated in 1972 [1]}. This conjecture states that if a graph \(G\)  is the union of \(n\)  cliques each of order \(n\)  with the condition that no two of them share more than one vertex, then \(\chi (G)=n\) . Although this is still an open problem, its fractional analogue was proved by Kahn and Seymour in 1992 [2]}. We refer the reader to [3]}, [4]} for more results on fractional colourings and on the fractional chromatic number.
